1. Field of the Invention
The present invention generally relates to a high rate Digital Subscriber Line (xDSL) modem, and more specifically, to a xDSL modem with a Carrierless Amplitude and Phase modulation (hereinafter, abbreviated as “CAP”) or Quadrature Amplitude Modulation (hereinafter, abbreviated as “QAM”) method which is configured to install a digital filter in front of an equalizer therein, thereby minimizing transmission errors generated by Bridged Tap (hereinafter, abbreviated as “BT”) of subscriber lines.
2. Description of the Prior Art
In a digital communication system, a transmission signal is easily distorted by a band-limited channel characteristic while passing through a transmission channel. This distortion is generated by gauss noise, thermal noise, impulse noise, additional or multiple noise due to a fading phenomenon where the strength of a signal varies depending on time, frequency change, non-linearity and temporal dispersion.
Adjacent symbols in the transmission signal are affected by the above-described distortion. This Inter-Symbol Interference (hereinafter, abbreviated as “ISI”) is a main cause to degrade performance of the communication system. Specifically, in a QAM system, the ISI is aggravated by multi-level characteristics, which results in obstacle to high-speed data communication.
The equalizer restores the transmission signal distorted by the ISI.
Recently, many researches have been made to solve the ISI. Of these researches, a Decision Feedback Equalizer (hereinafter, abbreviated as “DFE”) is proved to have the most excellent performance even in inferior channel conditions.
FIG. 1 illustrates a general structure of a VDSL modem with a conventional QAM or CAP method.
A transmission signal inputted through a channel 1 is distorted by noise n(t) such as additional white noise (AWGN) resulting from channel characteristics. The transmission signal affected by the noise n(t) is converted into a digital signal by an A/D converter 2.
The transmission signal converted by the A/D converter 2 is applied to a feed-forward filter (hereinafter, abbreviated as “FFF”) 3 of the DFE comprising a Finite Impulse Response (hereinafter, abbreviated as “FIR”) with a predetermined cycle to remove a precursor, and then applied to an adder 4.
The transmission signal, which is outputted from the FFF 3 and applied to the adder 4, is added with an output signal from a Feedback Filter (hereinafter, abbreviated as “FBF”) 6, and applied to a signal determiner 5.
The signal determiner 5 receives an output signal from the adder 4 to determine a level of the output signal.
The FBF 6 receives a value determined by the signal determiner 5 to remove a post-cursor of the value, and outputs the value whose post-cursor is removed into the adder 4.
FIG. 2 illustrates a structure of BT where a cable connected in parallel to a transmission channel is disconnected in a VDSL.
The BT generates null on a transfer function of the transmission channel.
A downward signal transmitted from a sending end 7 into a subscriber 8 is bridged in a bridged point B and reflected in a cross-section to be re-added in the bridged point B.
If a length of the BT is d, the transmission signal is transmitted by 2d through the BT. When a wavelength λ of a transmission signal satisfies d=λ/4 or 2d=λ/2, a phase difference of 180° occurs between a transmission signal which is bridged and retraced and a transmission signal which is not bridged. As a result, the two signals cause destructive interference from each other to remove a predetermined signal based on a corresponding frequency.
In other words, a null is generated on a channel transfer function as shown in FIG. 3 in a frequency having the wavelength A four times longer than the BT.
When a speed of a wave is v, the frequency f0 of a first null generated by the BT is expressed as follows.
                              f          0                =                              v            /            λ                    =                      v                          4              ⁢                                                          ⁢              d                                                          [Equation  1]            
Since the speed of the wave is determined by a medium, if the speed of light is c and an insulation constant of the medium is εr, Equation 1 is expressed as follows.
                              f          0                =                              v                          4              ⁢                                                          ⁢              d                                =                                    c                              4                ⁢                d                ⁢                                                      ɛ                    r                                                                        =                          K              d                                                          [Equation  2]            
Also, null is generated in the frequency of multiples of odd numbers of the null frequency f0, that is, in (2K+1)f0. As the length d becomes shorter, the depth of the null becomes deeper, thereby distorting the transmitted signal.
When the length of the channel is l, the channel transfer function of the subscriber line is generally expressed as follows.
                                                    H            ⁡                          (              f              )                                                =                              ⅇ                                          -                1                            ⁢                              α                ⁡                                  (                  f                  )                                                              ≈                      ⅇ                                          -                1                            ⁢              α              ⁢                              f                                                                        [                  Equation          ⁢                                          ⁢          3                ]            
Here, α(f) which represents a reduction constant of the line generally varies in the square root of frequency.
The Equation 3 can be expressed as Equation 4 since l is a reciprocating length 2d of the BT.
                                                    H            ⁡                          (              f              )                                                =                              ⅇ                                          -                2                            ⁢              d              ⁢                                                          ⁢                              α                ⁡                                  (                  f                  )                                                              ≈                      ⅇ                                          -                2                            ⁢              d              ⁢                                                          ⁢              α              ⁢                              f                                                                        [                  Equation          ⁢                                          ⁢          4                ]            
Since the first null frequency f0=K/d, the transfer function of the BT in the null frequency f0 can be represented as follows.
                                                                  H              bt                        ⁡                          (              f              )                                                =                  ⅇ                      -                          (                              2                ⁢                K                ⁢                                                                  ⁢                                  α                  /                                                            f                      0                                                                                  )                                                          [                  Equation          ⁢                                          ⁢          5                ]            
In Equation 5, if f0 becomes larger infinitely, that is, if the length of the BT becomes much shorter, the value of the transfer function of the BT is closer to 1. As a result, the transmission signal from the sending end 7 is remarkably reduced at the BT point B. In other words, the shorter becomes the length of the BT, the larger null is generated in a channel, which results in increase of transmission errors.
In the VDSL with a CAP or QAM method, the distortion on the transfer function is equalized by the DFE as shown in FIG. 1.
However, it is difficult to equalize deep null by a short BT unless the number of taps of the DFE is large. If the number of taps increases in order to solve this problem, the number of shift resistors also increases. As a result, hardware to the DFE becomes complicated, thereby increasing deciding delay time.
In addition, when the depth and width of the null are very large, it is difficult to minimize the transmission errors and to equalize the channel transfer function using the DFE.